Nope you are unlikely to sequence "all" your fragments since you sequence only a fraction of the library that you load on the flowcell.

You always sequence fragment)s). If you stop after sequencing one of the ends then that is all you get. If you happen to sequence from the other end they you get spatial information that tells you how long the original library fragment is. You can know this in two ways. If you have a reference genome you can map your reads to that genome and figure out how far apart they map. If you don't have a reference genome but your insert sizes are small then you can merge the two reads to create a longer representation that gives you the size if the insert. If you only start with 150 bp inserts and say do 2 x 100 bp paired end sequencing then your reads will overlap in the middle.